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A212504 Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y>2z.

%I A212504 #16 Mar 09 2016 05:26:57
%S A212504 0,0,0,7,24,76,162,333,576,976,1500,2275,3240,4572,6174,8281,10752,
%T A212504 13888,17496,21951,27000,33100,39930,48037,57024,67536,79092,92443,
%U A212504 107016,123676,141750,162225,184320,209152,235824,265591,297432
%N A212504 Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y>2z.
%C A212504 For a guide to related sequences, see A211795.
%H A212504 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F A212504 a(n) = 2a(n-1)+2a(n-2)-6a(n-3)+6a(n-5)-2a(n-6)-2a(n-7)+a(n-8).
%F A212504 From _Alois P. Heinz_, May 31 2012: (Start)
%F A212504 a(n) = A077043(n) * A002620(n-1) = ceiling(n^2*3/4) * floor((n-1)^2/4).
%F A212504 G.f.: x^3*(7+10*x+14*x^2+4*x^3+x^4) / ((x+1)^3*(1-x)^5). (End)
%p A212504 A212504:=n->ceil(3*n^2/4)*floor((n-1)^2/4); seq(A212504(n), n=0..40); # _Wesley Ivan Hurt_, Jan 24 2014
%t A212504 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212504 (Do[If[w < 2 x && y > 2 z, s = s + 1],
%t A212504 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212504 Map[t[#] &, Range[0, 40]]   (* A212504 *)
%Y A212504 Cf. A211795.
%K A212504 nonn,easy
%O A212504 0,4
%A A212504 _Clark Kimberling_, May 19 2012